Chapter 1 - Statistical Sampling
Hermione Granger was not like other girls her age. That much could be clearly illustrated - and had been - via simple bell curve charts based on surveys she'd given to her classmates. She'd asked how many books they'd read in the past year, how many books on average they read per week, and so on. In every relevant category, the dot that represented Hermione was sitting by itself off on the right side of the paper (except the chart showing school absences, where she was on the left, instead).
It was just as clearly (if more symbolically) illustrated in noting how few other girls had administered surveys, and that no one else at all had calculated the standard deviations. But that was something Hermione had learned early on.
At first, whenever she had a question, the path to answering it was simple - ask an adult, or find the right book. But she'd eventually discovered that there were some questions that weren't answered in books. Usually, because the question wasn't important enough that anyone else had asked it, or it was very specific. So she stepped back to the problem of question-answering in general, and there were a great many books about that. They were so interesting, in fact, that she couldn't remember what question she'd wanted to answer in the first place when she'd come up for air a week or so later.
But now she had some tools for figuring such things out, even if other people seemed to use them even less than they used books. Of course, these tools had their own difficulties at times. Take statistical sampling, for example. You needed a large enough pool of examples before you could be at all confident about any patterns you thought you saw. That began to become troublesome when Hermione's classmates started answering her surveys unhelpfully, or even untruthfully. They seemed to think it was funny (and based on the proportion of students who laughed, objectively it probably was funny, even if it didn't seem like it to her).
There were questions that were hard to pin down for other reasons, though. She'd begun to notice...odd things. Coincidences, you could call them, taken individually. Sometimes when she was particularly excited to look something up, the book she wanted seemed to leap off the shelf into her hand before she'd really pulled on it at all. The time she'd been having trouble tuning out other students' chattering at school while she read, then suddenly gone deaf for half the day. The horrifying occasion when she'd accidentally torn the page of a library book - or thought she had - but when she looked at it again, the page was quite unblemished.
How could you account for that, though? Unlikely things didn't happen very often taken in isolation, but collect a few million people and have them do a few dozen things every day, and they happened to everyone, all the time. Just because Hermione seemed to notice more pleasant coincidences than not didn't mean that formed a real pattern. The idea of 'luck' was just a combination of superstition and people not understanding probability.
Besides, for every minor thing she might call mildly lucky, there were other examples of misfortune. Her front teeth, for example, protruded a bit. When other children had teased her about them, she'd done her best to ignore it, but she'd also naturally looked at a few books, and it seemed like something easily fixed with orthodontia. Yet when she'd brought it up to her parents - who were dentists, after all - she got nowhere. They seemed to think orthodontists were stuck-up and unjustly full of themselves and were thus quite against employing them for any reason.
Still, the question of these coincidences remained, tucked in the back of her head along with a few other open mysteries, like what caused differences in individual preferences (specifically, why so few other students ever cared to raise their hands in class), or why it was so hard for her to make friends. Things she kept lightly in mind, just in case she happened to read some odd fact or theory that might clear everything up.
One summer afternoon in 1991, after receiving a certain Letter, she did in fact read something that purported to clear everything up. However, considering it did so by suggesting that nearly a third of everything else Hermione had ever read was wrong (or at least woefully incomplete), it was rather difficult to accept at face value.
Of course, it was possible it was just a prank - she'd been on the receiving end of many over the years - though if so it had required rather more research than anyone had gone to previously. It had been addressed with peculiar specificity, down to the position of her bedroom (First Bedroom on the Left, Second Floor), which, to her knowledge, none of her classmates knew, as she'd never had occasion to invite any of them over. But it would not have been all that difficult to find out if someone had been properly determined.
If it was a prank, however, she didn't see what the payoff would be, seeing as the letter had advised her to expect a school representative to arrive at her home in three days to 'explain the situation more fully' to her and her parents. If it had said she was to post a ten pound note 'for registration' or to go to some remote location where pranksters might show up and pelt her with toads or something similarly imaginative, that might have made more sense. But surely no prankster would be eager to face Mr. and Mrs. Granger, who were no-nonsense sort of people, and likely to give short shrift to any such shenanigans, particularly at their own home?
She'd have just asked her parents, but they were still at work, and the Letter gnawed at her, so naturally, she walked to the local library. After a couple hours of very interesting reading (primarily in the New Age and History sections), she'd decided that believing in things that didn't provide much helpful evidence was probably an effective way of practicing creativity, as the latter gave a strong showing in books on 'practical magic' while the former was seemingly absent. Nor was there any hint of the existence of any school called 'Hogwarts', past or present.
Two hours in a library might have exhausted the patience, curiosity (or likely, both) of an average eleven-year-old, but Hermione had been gifted with perseverance to match her intelligence, and she was not nearly inclined to give up yet - though unfortunately she didn't have much time before her parents were due home for dinner. Accordingly, she went to the reference desk and got the telephone numbers for every government agency she thought might be relevant to a school for magic, then walked home.